Solve x+6/9x^2-3x+10/15x^2

$$\frac { x + 6 } { 9 x ^ { 2 } } - \frac { 3 x + 10 } { 15 x ^ { 2 } }$$

Evaluate

$$-\frac{4}{45x}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 9x^{2} and 15x^{2} is 45x^{2}. Multiply \frac{x+6}{9x^{2}} times \frac{5}{5}. Multiply \frac{3x+10}{15x^{2}} times \frac{3}{3}.

$$\frac{5\left(x+6\right)}{45x^{2}}-\frac{3\left(3x+10\right)}{45x^{2}}$$

Since \frac{5\left(x+6\right)}{45x^{2}} and \frac{3\left(3x+10\right)}{45x^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5\left(x+6\right)-3\left(3x+10\right)}{45x^{2}}$$

Do the multiplications in 5\left(x+6\right)-3\left(3x+10\right).

$$\frac{5x+30-9x-30}{45x^{2}}$$

Combine like terms in 5x+30-9x-30.

$$\frac{-4x}{45x^{2}}$$

Cancel out x in both numerator and denominator.

$$\frac{-4}{45x}$$

Expand

$$-\frac{4}{45x}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 9x^{2} and 15x^{2} is 45x^{2}. Multiply \frac{x+6}{9x^{2}} times \frac{5}{5}. Multiply \frac{3x+10}{15x^{2}} times \frac{3}{3}.

$$\frac{5\left(x+6\right)}{45x^{2}}-\frac{3\left(3x+10\right)}{45x^{2}}$$

Since \frac{5\left(x+6\right)}{45x^{2}} and \frac{3\left(3x+10\right)}{45x^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5\left(x+6\right)-3\left(3x+10\right)}{45x^{2}}$$

Do the multiplications in 5\left(x+6\right)-3\left(3x+10\right).

$$\frac{5x+30-9x-30}{45x^{2}}$$

Combine like terms in 5x+30-9x-30.

$$\frac{-4x}{45x^{2}}$$

Cancel out x in both numerator and denominator.

$$\frac{-4}{45x}$$